An improved nonlinear proportional-integral-differential controller combined with fractional operator and symbolic adaptation algorithm

Abstract

Parameter adjustment is usually applied for designing the proportional-integral-differential (PID) controllers. However, the ability to improve control performance by adjusting parameters is limited. Hence, with the goal to achieve ideal closed-loop response, this paper takes advantage of a structural optimization method for modifying the controller model. A symbolic adaptation algorithm for fractional order PID (FOPID) controller is employed to obtain precise nonlinear controller model. Firstly, a modeling comparison for nonlinear duffing system is carried out to highlight the efficiency of the symbolic adaptation algorithm. The case study indicates the proposed algorithm can establish compact dynamic models by amending the shortcomings of symbolic regression. Secondly, the proposed controller is restructured with the linear FOPID controller and its nonlinearity is increased by adjusting controllers’ components in symbolic form. The proposed controllers are simulated in an unstable second-order system, a time-delay system and a nonlinear VanderPol system. Compared with the IOPID and the FOPID controller, the symbolic adaptation algorithm improves the structural flexibility of these linear controllers. Meanwhile, the system response can better approximate the desired response and the structural integrity of the nonlinear controller model is guaranteed simultaneously. Finally, the nonlinear FOPD controllers for trajectory tracking experiments are carried out on a rotary inverted pendulum control system.

Add-on integration module-based proportional-integration-derivative control for higher precision electro-optical tracking system

“…The magnitude optimum criterion is applied to the PID controller to improve system load disturbance rejection in Cvejn and Vrančić (2018). To achieve ideal closed-loop response, the fractional order PID controller is employed to a rotary inverted pendulum control system in Shi et al (2020). All of these tuning rules for PID provide theoretical support for their application in practical engineering.…”

An Adaptive Super Twisting Nonlinear Fractional Order PID Sliding Mode Control of Permanent Magnet Synchronous Motor Speed Regulation System Based on Extended State Observer

“…Compared with Integer-order, the extra degrees of freedom from using of Fractional-order integrator and differentiator made it possible to further improve the control effect [35]. Recently, many SMC strategies based on different forms of LFOPID sliding surface have been widely used in many systems, such as wind power generation system [36], wheeled mobile robot [37], electro-hydraulic servo system [38] and PMSM [39], et al However the linear superposition of three basic modules in the LFOPID can cause the contradiction between the rapidity and the overshoot, and the LFOPID also has the disadvantages of simplicity and tough, which makes it difficult to meet the control requirements of high quality [40], [41]. A nonlinear function fal(•) was proposed by Han in [42].…”

A Novel Model-Free Intelligent Proportional-Integral Supertwisting Nonlinear Fractional-Order Sliding Mode Control of PMSM Speed Regulation System

“…e FOSMC scheme has widely been used in many fields such as robot manipulator [27], doubly fed induction generator-based wind farm [28], PMSM position regulation system [29], microgyroscope [30], stand-alone modern power grids [31], and fractional-order complex systems [32]. However, the conventional FOSMC has the disadvantages of simple and rough signal processing to limit its application [33][34][35]. We presented the nonlinear fractional-order sliding mode controller (NLFOSMC), which can effectively settle the abovementioned issues [36][37][38].…”